Heretofore, the mythology of Supernatural has been consistent with the traditional and pretty much globally universal notion among believers in the soul, common to Plato, Augustine, and Descartes, that, not to make too much of subtle distinctions among views (pace, Thomists), the soul is the self.
Hence the immortality of the soul is that of the self, of one's-self.
Hence eternity in hell or an eternity of transmigrations of one's soul are an eternity in hell, or of transmigrations, of oneself.
And that is the view espoused by the alpha vampire in Season 6, Episode 7, though in this episode we discover that Sam was released from the chamber in hell containing Lucifer and Michael and sent back to Earth without his soul, which remains imprisoned with them.
That makes him maybe a Cartesian fake, a machine without a soul - or a person in the view of La Mettrie.
Or maybe a philosophical zombie.
But it doesn't seem to make much difference in him, except that he lacks all people-sense, both as understanding and as empathy.
At first, he insists he is himself, has all the right memories and personality traits and so on.
But by the end of the episode he admits he isn't Sam, that without his soul he's not the same person at all.
Though what that seems to mean is that without his usual dose of empathy Sam is as different from his prior self as Hannibal the Cannibal is from Clarice.
And it's as mystifying to others in the show as it is to us.